Array vs List

Performance wise, there won't be a difference in the method call - all that is passed is a single reference in either case.

Which is best?
Depends on what you are doing. If it is a fixed array of strings, where the number of strings is known at compile time, and they do not change number, content or order at run time, then an array may be best.

If the number is not known, then List. If the order or number of items changes, List.

There is no "best" solution - it will depend on your code, and what you are trying to achieve. Bear in mind that a List can be converted to an array at any time...

If the function needs purely readonly access to the collection, you could use IEnumerable<string> or ReadOnlyCollection<string>. That way it will not be able to modify the collection. With the array, the risk is merely that of modified entries, the length cannot be changed. With the list, in addition to the risk of modified entries, the function can also remove/add entries and thus change the length of the collection. So there's that to consider too.